Question: Simplify the following expression: $p = \dfrac{40k - 72}{16k - 16}$ You can assume $k \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $40k - 72 = (2\cdot2\cdot2\cdot5 \cdot k) - (2\cdot2\cdot2\cdot3\cdot3)$ The denominator can be factored: $16k - 16 = (2\cdot2\cdot2\cdot2 \cdot k) - (2\cdot2\cdot2\cdot2)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $p = \dfrac{(8)(5k - 9)}{(8)(2k - 2)}$ Dividing both the numerator and denominator by $8$ gives: $p = \dfrac{5k - 9}{2k - 2}$